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Debby filled 10 times as many buckets of water as Marty, and Melissa filled 6 times as many buckets as Marty. All
3 together filled 136 buckets of water to fill a pool. How many buckets did Marty fill?

Respuesta :

ANSWER

Marty filled 8 buckets of water

EXPLANATION

Let

• x: number of buckets Marty filled

,

• y: number of buckets Debby filled

,

• z: number of buckets Melissa filled

We know that Debby filled 10 times as many buckets as Marty:

[tex]y=10x[/tex]

And that Melissa filled 6 times as many buckets as Marty:

[tex]z=6x[/tex]

All three of them together fulled 136 buckets:

[tex]x+y+z=136[/tex]

Replace y and z as functions of x:

[tex]x+10x+6x=136[/tex]

And solve for x. First add like terms:

[tex]\begin{gathered} (1+10+6)x=136 \\ 17x=136 \end{gathered}[/tex]

And divide both sides by 17:

[tex]\begin{gathered} \frac{17x}{17}=\frac{136}{17} \\ x=8 \end{gathered}[/tex]

We found that Marty filled 8 buckets of water.

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